Reaction of the nonlinear Dirac equation to a nonlinear Schrodinger equation with a correction term

We examine the low-energy limit of the nonlinear Dirac equation (NLDE) in 1+1 dimensions with a Lorentz scalar self-interaction. Unlike the nonlinear Schrodinger equation (NLSE), which is integrable, the NLDE is known to exhibit rich dynamics of the soliton-soliton collision when the relative speed of the solitons is small. The NLDE is intrinsically different from the NLSE even when the energy involved is small. When it is modified by adding a specific correction term, however, the NLSE well reproduces the complex features of the soliton-soliton collision described by the NLDE.